@ Nicky. I think you are correct with your estimate of 3 to 4KW required.
My 6/1 drives a 3KW gen head which easily starts my 3/4Hp deep well pump. That's the biggest single load in my system.
It is an Utterpower PMG though, so is an overbuilt/underrated gen head.
I did have a 4.5KW Honda generator, it would also start the well pump, but was working hard.
The 6/1 with the PMG barely notices. Heavy flywheels help.
Cheers
Hugh